Stern–Gerlach Experiment

The Stern–Gerlach experiment sends neutral atoms through an inhomogeneous magnetic field and observes discrete beam splitting. In modern language, it is a prototype for measuring a spin component along a chosen axis.

The original silver-atom experiment is not literally a measurement of a free electron’s spin alone; the modern spin-$1/2$ idealization keeps the formal lesson while simplifying the atomic physics.

Formula Hook

For a magnetic moment in a magnetic field,

$$H = - \boldsymbol\mu\cdot\mathbf B.$$

For a spin-$1/2$ degree of freedom, the component along direction $\hat{\mathbf n}$ is

$$S_{\hat{\mathbf n}} = \frac{\hbar}{2}\sigma_{\hat{\mathbf n}},$$

with possible ideal measurement outcomes

$$\pm\frac{\hbar}{2}.$$

Changing the apparatus orientation changes the measured operator.

Canonical Home

This glossary entry is the current named-experiment home. For the formal spin lesson, see What Spin Is, Spin-1/2 Hilbert Space, Pauli Matrices, and Measurement in the Formalism.

Common Confusions

• The two spots are not evidence for a tiny classical arrow that always had a definite direction in space.
• The measured component depends on the magnet orientation.
• Sequential Stern–Gerlach measurements along different axes illustrate noncommuting observables.
• Real apparatus modeling involves field gradients, atomic structure, beam collimation, and detection, beyond the ideal projective-measurement model.

Related Entries

• Eigenstate
• Observable
• Zeeman Effect

References

• W. Gerlach and O. Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift fuer Physik 9, 349-352, 1922.
• B. Friedrich and D. Herschbach, “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics,” Physics Today 56, 53-59, 2003.
• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.